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{SECT 0 {PARA 208 "" 0 "" {TEXT 200 0 "" }{TEXT 200 0 "" }{TEXT 200 9 
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4 "" 0 "" {TEXT 221 14 "Line integrals" }}{EXCHG {PARA 0 "" 0 "" {TEXT
 200 63 "The \"LineInt\" command can be used to evaluate line integral
s." }{TEXT 200 55 "  The syntax for the \"LineInt\" command is as foll
ows:" }}{PARA 0 "" 0 "" {TEXT 200 0 "" }}{PARA 212 "" 0 "" {TEXT 200 
24 "LineInt( VectorField( < " }{TEXT 216 6 "P(x,y)" }{TEXT 200 3 " , "
 }{TEXT 217 6 "Q(x,y)" }{TEXT 200 14 " > ), Path( < " }{TEXT 218 4 "x(
t)" }{TEXT 200 3 " , " }{TEXT 219 4 "y(t)" }{TEXT 200 9 " >, t = t" }
{TEXT 200 1 "1" }{TEXT 200 3 "..t" }{TEXT 200 1 "2" }{TEXT 200 2 "))" 
}}{PARA 213 "" 0 "" {TEXT 200 0 "" }}{PARA 0 "" 0 "" {TEXT 200 161 "In
 order to be able to use the \"LineInt\" command, you must first tell \+
Maple in which coordinate system you are working.  To do this, use the
 following command:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "SetC
oordinates(cartesian[x,y]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 113 "Now we are able to use t
he \"LineInt\" command to check, for example, if the formula in Proble
m 16.4b is correct:" }}{PARA 0 "" 0 "" {TEXT 200 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 52 "LineInt( VectorField( <-y,x> ), Line( <a,
b>,<c,d>));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 37 "This matches the formula (of
 course)." }}{PARA 0 "" 0 "" {TEXT 200 0 "" }}{PARA 0 "" 0 "" {TEXT 
200 120 "For Problem 16.4e, you will need to find the line integral al
ong the parabola, along the line segment; add the results. " }}{PARA 0
 "" 0 "" {TEXT 200 82 "Then use Green's theorem. The answers obtained \+
by both methods should be the same." }}{PARA 0 "" 0 "" {TEXT 200 0 "" 
}}{PARA 0 "" 0 "" {TEXT 200 50 "Let us do the line integral along the \+
parabola.   " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "LineInt( Ve
ctorField( <x^3*y,-x^2*y^2> ), Path(<1-t,(1-t)^2-4>, t=0..2));" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 200 69 "So now you know what to expect wh
en you compute the integral by hand." }}}{EXCHG {PARA 0 "> " 0 "" 
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